Question

A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 8 feet. The area of the logo must be at least 36 square feet. (The logo has to be seen from all the seats.) Write an inequality that describes the possible base lengths (in feet) of the triangle.

Use b for the base length of the triangular logo.

SOMEONE PLS HELP ME! THANK YOU!

Answer 1

`b\geq 9`

In other words, the base must be at least 9 feet long.

Explanation:

The schools wants the height of the triangle to be eight feet, and the area of the logo to be at least 36 square feet.

Recall that the area of a triangle is given by:

`\displaystyle A = (1)/(2)bh`

Since we want to area to be at least 36 square feet:

`\displaystyle (1)/(2)bh \geq 36`

We are given that the height is eight feet. Substitute:

`\displaystyle (1)/(2)(8)b\geq 36`

Simplify:

`4b\geq 36`

Divide both sides by four. Hence, our inequality is:

`b\geq 9`

In words, this means that the base must be at least 9 feet long.